In the past years, a flowmeter measuring the mass flow rate of media employing a single or a pair of vibrating conduits, that is commonly known as the Coriolis force flowmeter or the convective inertia force flowmeter, has become quite popular and scored a spectacular success in the field of industrial flow measurements. The existing versions of this type of mass flowmeter comprising a single or a pair of the vibrating conduits of U-shaped, S-shaped or looped construction are unreasonably expensive, and their designs as well as constructions are not suitable for the mass flowmeters of sizes greater than a two inch port diameter in all practical senses. The present invention teaches the mass flowmeters employing a single or a pair of vibrating conduits, which provides an alternative to the existing versions of the mass flowmeters in terms of the cost, improved sensitivity and/or better feasibility in design to construct the mass flowmeters of large port sizes.